Freedericksz Transition Research Articles

Freedericksz transition in a nematic cell with periodic anchoring energy in electric field

The threshold value and shape of the spatially inhomogeneous threshold distribution of the director in an electric field in a planar nematic cell with periodic polar nematic anchoring energy with the cell surface have been determined. It is shown that the threshold value depends nonmonotonically on the number of anchoring energy periods per cell length. An analytical expression for the Freedericksz transition threshold at small anchoring energy modulation amplitudes is obtained, and a numerical calculation of threshold values at large amplitudes is performed. The spatial period of the director structure arising at Freedericksz transition depends strongly on the ratio of Frank elastic constants (K2/K1) and the number of anchoring-energy modulation periods per cell length, but is hardly affected by the anchoring energy modulation amplitude.

Valinomycin-induced pore formation in thin lipid film and its effect on splay and bend elastic constant

AbstractValinomycin-induced rapid changes in the orientation patterns of lipid molecules under an applied field were observed in 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DPPC) thin films, aligned on polyvinyl-alcohol-coated indium tin oxide (ITO) glass electrodes both below (Lβ) and above (Lα) phase transition temperatures of DPPC. With the increasing concentration of valinomycin, Freedericksz's transition patterns change significantly. The values of splay (κ11) and bend (κ33) elastic constant changed by several orders of magnitude depending upon the concentration of valinomycin in the DPPC thin films. From the micrographs of field emission scanning electron microscopy, it was clear that pore formation on DPPC thin films would be a reason behind the decay of elastic constant. The decay of elastic constant was described by an exponential decay formula, y = A1e−x/t1+y0. From this point of view, we propose that our system can be used as a biosensor to detect antibiotic-like valinomycin.Keywords: valinomycinFreedericksz's transitionbiosensorlipid aggregatesmembrane elasticity AcknowledgementsThe helpful discussion with Dr Ashesh Nandy and Dr Smarajit Manna, Centre for Interdisciplinary Research and Education, and Dr Suman Bhandary, Bose Institute, are acknowledged.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingWe thank Defense Research and Development Organization (DRDO), Defense Ministry, India, for their financial support [grant number: ERIP/ER/1103954/M/01/1413].

Energy Minimization for Liquid Crystal Equilibrium with Electric and Flexoelectric Effects

This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of free energy based on the electrically and flexoelectrically augmented Frank--Oseen free energy models. The Hessian, resulting from the linearization of the first-order optimality conditions, is shown to be invertible for both models when discretized by a mixed finite-element method under certain assumptions. This implies that the intermediate discrete linearizations are well-posed. A coupled multigrid solver with Vanka-type relaxation is proposed and numerically vetted for approximation of the solution to the linear systems arising in the linearizations. Two electric model numerical experiments are performed with the proposed multigrid solver. The first compares the algorithm's solution of a classical Freedericksz transition problem to the known analytical solution and demons...

Electrical Freedericksz transitions in nematic liquid crystals containing ferroelectric nanoparticles

A new theoretical approach was elaborated to explain the contradictions reported in many papers about the electric threshold for Freedericksz transition in nematic liquid crystal (NLC) with ferroparticles additives. The free energy density of the mixture was estimated and the contributions of the interaction energy of NLC molecules with ferroparticles surface were calculated. Experimental results for 5CB-BaTiO3 mixture are given.

Light-controlled electric Freedericksz threshold in dye doped liquid crystals

We report the results of measurements of the threshold of Freedericksz transition in a nematic liquid crystal doped by Methyl-red. We show that in case of dc field the threshold voltage can decrease or increase depending on the light dose, due to the light-induced desorption and adsorption of charge complexes from and on the irradiated surface, that has been recently demonstrated. This effect has the potential to be exploited in optical devices such as liquid crystal microlenses and spatial light modulators.

Determination of elastic constants of a binary system (7CPB+9.CN) showing nematic, induced smectic Ad and re-entrant nematic phases

The temperature variation of the splay and bend elastic constants of a binary system exhibiting nematic-induced smectic Ad and re-entrant nematic phases measured by electric field-induced Freedericksz transition method has been reported. As bend deformation is not permitted in the smectic A phase, bend elastic constant (K33) could only be determined in the nematic and re-entrant nematic phases. In both the nematic phases, the splay elastic constant has the same order of magnitude and does not show any pretransitional effect. However, in the induced smectic Ad phase, the value of K11 is about one to two orders higher than that in the nematic phases. The bend elastic constant shows a strong pretransitional effect near the nematic–smectic and smectic–re-entrant nematic phase transitions. The influence of the presence of the induced smectic phase is observed even in those mixtures which have no induced smectic phases. As the smectic phase is approached, the ratio K33/K11 increases rapidly and diverges to infinity.

Light-induced orientation of the molecules of nematic liquid crystals doped with comb-shaped polymers with different spatial distributions of chromophores

The orienting effect of light on nematic liquid crystals (NLCs) doped with comb-shaped polymers with different spatial distributions of side absorbing azobenzene fragments, i.e., a homopolymer (containing only azofragments), a block copolymer (containing additionally a block of non-absorbing fragments), and a statistical copolymer (containing randomly arranged absorbing and non-absorbing fragments) is experimentally studied. The light-induced Freedericksz transition threshold for the block copolymer is two times lower than that for the homopolymer. For NLC with statistical copolymer dopant, the first-order orientation transition with an extremely wide optical bistability region is observed.

Magnetic control of flexoelectric domains in a nematic fluid.

The formation of flexoelectric stripe patterns (flexodomains) was studied under the influence of external electric and magnetic fields in a nematic liquid crystal. The critical voltage and wavevector of flexodomains were investigated in different geometries by both experiments and simulations. It is demonstrated that upon altering the orientation of the magnetic field with respect to the director, the critical voltage and wavenumber behave substantially differently. In the geometry of the twist Freedericksz transition, a non-monotonic behavior as a function of the magnetic field was found.

Specific features of the freedericksz transition in nematic-cholesteric droplets: The effect of the liquid crystal-isotropic phase boundary

Quasi-static orientation transitions in nematic-cholesteric liquid crystal (LC) droplets occurring in an isotropic environment in a constant electric field have been studied. It is shown that transformation of the initial homeotropic orientation of the director field in these LC droplets has a non-threshold character, which is related to the presence of a small cholesteric additive. As the field increases, this dopant leads to continuous growth in the effective size of a deformation field from the LC-isotropic phase interface.

A Quantitative Measurement of Wall Shear Stress Using Electric Capacity Sensing of Nematic Liquid Crystal Coating

The measurement of wall shear stress (WSS) still remains a challenge in many fields such as fluid hydrodynamics, microfluidics, or biomechanics. The nematic liquid crystal coating (LCC) is a prospective technique to measure WSS due to its global measurement capability, high resolution, and non-intrusive nature. But its current application based on the optical observation is severely limited by the requirement for a complex system. In this paper, we invented a novel WSS-measuring technique based on the anisotropic permittivity and the Freedericksz transition of nematic LCC under shear stress. First, a quantitative model was built to describe the reorientation responses of nematic liquid crystal molecules under shear stress, and the corresponding variation in dielectric property of LCC was derived. Thus, the quantitative relationship between WSS and the electric capacity output of LCC was obtained. Then, an LCC sensor was fabricated using spin coating and microlithography to verify the engineering feasibility in WSS measurement. The experimental results of capacity variation are in good agreement with the theoretical molecular model of LCC under shear stress. The mechanism and advantages of the capacity-sensing LCC technique were discussed in view of quantitative and wide-ranged WSS measurement: easy and reversible initialization, as well as potential on-site applications.

Dynamics of a liquid crystal close to the Fréedericksz transition

We study experimentally and numerically the dynamics of the director of a liquid crystal driven by an electric field close to the critical point of the Fréedericksz transition (FT). We show that the Landau-Ginzburg (LG) equation, although it describes correctly the stationary features of FT in a rather large range of the control parameter, cannot be used to describe the dynamics in the same range. The reasons of this discrepancy are related not only to the approximations done to obtain this equation but most importantly to the finite value of the anchoring energy and to small asymmetries on boundary conditions. The difference between static and dynamics is discussed. These results are useful in all of the cases where FT is used as an example for other orientational transitions.

Nonlinearities induced by magnetic fields in nematic liquid crystals

We investigated a nonlinear phenomenon arising when a planar oriented NLC cell introduced into a magnetic field was subjected to a laser beam with normal incidence. The limit number of diffraction rings was measured for different magnetic fields, higher than the critical one for the magnetic Freedericksz transition. A dynamical measurement of the fringes number was made for a magnetic field equal to the one for which the maximum number of rings was obtained. Another dynamical measurement was made for a higher field and, in all the cases, the theoretical approach was in good agreement with experimental data.

First-order optical Freedericksz transition in a dye-doped nematic liquid crystal

A first-order optical Freedericksz transition in a nematic liquid crystal doped by a small quantity of a dichroic dye with negative dichroism is observed. The initial homeotropic state corresponds to maximum absorption for the linearly polarized incident beam, while reorientation reduces absorption increasing the optical torque: this process produces the positive feedback leading to the observed bistable behavior.

Evolution of the discontinuous anchoring transition under an electric field

Anchoring transition (ATr), resulting in the orientational change of liquid crystal (LC) molecules at surfaces with temperature variation, is shown to be essentially affected by the application of an electric field (E field). By combining defocusing polarizing microscopy with retardation measurement, a detailed investigation of the molecular orientational change in the vicinity of ATr during a cooling process under an E field was performed. Two important conclusions can be made from our observations: (i) the ATr temperature exhibits a large downshift in the presence of an E field; (ii) the orientational change is always discontinuous from a planar (P) state to a homeotropic (H) state. If the applied E field is below the Freedericksz transition, P and H states are uniform, whereas the surface H state is influenced by the tilt in the bulk due to negative dielectric anisotropy, resulting in a bent-splay deformed state.

Study of light-induced reorientation of the nematic liquid crystal director by birefringence dynamics

It is proposed to apply the birefringence method to measure the threshold of the light-induced Freedericksz transition and the nonlinearity enhancement factor of nematic liquid crystals by director relaxation dynamics in the light field. A birefringence change is recorded by interference of ordinary and extraordinary components of the light beamaffecting the liquid crystal director orientation. The Freedericksz transition thresholds and nonlinearity enhancement factors are measured for the samples doped with comb-shaped polymers with various degrees of polymerization. The determined thresholds are in agreement with the results obtained by the aberrational self-action method.

Increasing the magnetic sensitivity of liquid crystals by rod-like magnetic nanoparticles

Magnetic Freedericksz transition was studied in ferronematics based on the nematic liquid crystal 4-(trans-4'-n-hexylcyclohexyl)-isothiocyanatobenzene (6CHBT). 6CHBT was doped with rod-like magnetic particles of different size and volume concentration. The volume concentrations of magnetic particles in the prepared ferronematics were $\phi_1$ = 10$^{-4}$ and $\phi_2$ = 10$^{-3}$. The structural changes were observed by capacitance measurements that demonstrate a significant influence of the concentration, the shape anisotropy, and/or the size of the magnetic particles on the magnetic response of these ferronematics.

The elastic and optical properties of a bent-core thiadiazole nematic liquid crystal: the role of the bend angle

The elastic and optical properties of a bent-core thiadiazole nematic liquid crystal are reported. The system exhibits unusually large values of birefringence (∼0.4), which can be partly attributed to significant conjugation in the molecular structure. It is found that the splay (K11), twist (K22) and bend (K33) elastic constants, determined from studies of the Freedericksz transition, satisfy K33 > K11 > K22 across the wide nematic range studied. Such behaviour is analogous to that commonly observed in calamitic nematic liquid crystals but is in contrast to all other bent-core nematic materials reported to date where it is found that K33 < K11. Such a result questions some of the current explanations that have been put forward to explain the elastic behaviour of bent-core materials. Using a molecular field theory, combined with DFT calculations of the molecular structure, we can ascribe the different elastic behaviour to the value of the bend angle in the molecular core. This angle is shown to play a subtle and substantial role in determining the physical properties of bent-core nematic liquid crystals.

Influence of the anchoring energy on hysteresis at the Freedericksz transition in confined light beams in a nematic cell

The influence of the finite value of a nematic director anchoring energy on the hysteresis of the light-induced Freedericksz transition induced by a normal incident linearly polarized one-dimensional bounded light beam is considered. The intensity distribution throughout the cross section of the beam is described by a Heaviside function. Values of the Freedericksz transition threshold and the director deviation angle jumps with increasing and decreasing incident light intensity are numerically obtained and are dependent on the director anchoring energy magnitude and the light beam cross section. Allowable regions of the light beam widths, anchoring energy values and values of the parameters , at which the Freedericksz transition is accompanied by hysteresis are determined.

Influence of the segregation effect on the magnetic and optical properties of a compensated ferronematic liquid crystal

The Freedericksz transition in splay and bend geometry in a ferronematic (a suspension of single-domain magnetic particles in a nematic liquid crystal) is considered in the framework of the continuum theory. In zero magnetic field, the ferronematic was assumed to be compensated (i.e., having equal fractions of an impurity with magnetic moments directed parallel and antiparallel to the local director). Spatial distortions of the director and the concentration redistribution of the magnetic impurity in the ferronematic layer are studied as functions of the applied magnetic field and the segregation parameter. It is shown that the magnetic-field induced Freedericksz transition from the homogeneous to the inhomogeneous state has a threshold nature. The transition field as a function of the material parameters of the ferronematic is determined analytically. Magnetization of the ferronematic and its optical properties for a strong and weak segregation as functions of the magnetic field are studied.

Light Interaction with NLCs Doped with Comb-Shaped Azopolymers with Different Degrees of Polymerization

The light-induced director reorientation in NLCs doped with the comb-shaped azopolymers with different degrees of polymerization (the number of chromophore groups) has been studied. The negative optical nonlinearity (a decrease in the refractive index of the extraordinary wave due to the director rotation away from the light field) was observed for all dopants. It was found that the threshold power of the Freedericksz transition decreases with the polymerization degree. The light-induced Freedericksz transition of the first order was observed for the dopants with lower degrees of polymerization.